GLOBAL ASSOCIATION OF RISK PROFESSIONALS40 MARCH/APR IL 08 I SSUE 4411

One of the most obvious features of financialmarkets is that prices move up and downunpredictably. This has led to random walkmodels that, in turn, suggest that practition-ers should look for insight to games based onrandomization: e.g., coin flips, dice rolls and

card shuffles. In this article, I’d like to look at risk analysisfrom a chess master’s perspective. I’ll try to compare chessanalysis to risk analysis and explain what risk managementmight learn from chess.

Although chess has no randomness or concealed infor-mation, it is nonetheless unpredictable. If two players sitdown to play a game of chess, neither the game nor theresult is the same as the game the same two players playedyesterday.

Imagine a risk manager and a hedge fund manager tryingto decide an appropriate leverage level for a portfolio andtwo opposing chess masters trying to decide how compli-cated they want their positions to be. Are there no similari-ties? Let’s see.

How does chess resemble risk analysis? Are there similarities, for example, between the way a chess playerstudies opponents’ games and the way a risk analyst studies clients’ portfolios? Igor Postelnik takes acomprehensive look at chess strategy and discusses the lessons that risk managers can learn from chess.

Chess: A Valuable TeachingTool for Risk Managers?

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Just as higher leverage may enhance return or cause big-ger loss for a risk manager or a hedge fund manager, amore complicated chess position may open unexpectedvariations that will lead to first-prize money or leave aplayer without a prize at all. Each chess move has advan-tages and disadvantages. While each move’s advantagesinclude creating the possibility of a certain desirable futureline of play, there is a risk that each move will open up pos-sibilities for (perhaps unforeseen) lines of play that aredesirable for the other side. Weighing the risks of this playand counterplay is the key to good judgment in chess and isreally a type of risk management.

Before moving forward, let me dispel a myth that chess isa deterministic game with full information available toboth players. In theory, this is true. However, in practice, itis hardly ever the case that a player sees all possibilities atonce. And even if he or she actually sees them, it’s hard topredict how well an opponent willreact to them. So, it comes down toprobabilities: i.e., how likely is theopponent to know a certain open-ing or a certain type of a position?

For example, I am a 2200-ratedchess player. Against someone ratedbelow 2000, I definitely prefer toreach a simple position as soon aspossible. Against someone ratedabove 2400, I want to keep theposition very complicated for aslong as possible.

As more pieces come off the board, the less room there isfor calculations. Why does it matter? A simple positiondoesn’t require deep calculations but does require a deepunderstanding of strategy. Chess players, as their strengthgrows, learn to calculate first and understand later.

In risk management, an analyst takes a first look at afund's portfolio (chess position) and has to make a firstmove (approve for leverage). Once a certain level of lever-age is approved (the first move is made), we have to consid-er how the portfolio manager will respond — as well aswhat factors will cause the trader to complicate the posi-tion (increase risk in the portfolio) and, when that happens,how the risk manager should respond.

There are other similarities between chess strategy andrisk analysis. Under time pressure in a tough position, achess player has to choose a move, while a risk managerhas to choose a position in the portfolio to liquidate tomeet a margin call when a portfolio is tanking. Chess play-ers also study opponents’ games trying to anticipate howthe next game will develop, while risk analysts studyclients’ portfolios trying to anticipate how the next tradewill affect the portfolio.

Humans vs. ComputersA complicated chess position requires deep calculationsand is more likely to cause a human player to make anerror. The players understand this general guideline, butalso study their future opponents’ games and try to pick astyle that is least familiar to their opponent. In 1997, forexample, while Garry Kasparov was preparing to play acomputer, IBM programmers and chess advisers hadadjusted Deep Blue to better analyze Kasparov’s previousgames. The styles that are most effective for Kasparov areknown in the chess world, so the computer program wasfine-tuned to avoid playing such styles. By analogy, a com-puter risk model needs to be fine-tuned to better analyzestyles a fund manager is more likely to use.

Deep Blue didn’t just play a game. It played against aspecific opponent’s style, and Kasparov was embarrassing-ly crushed in the last game as a result. Similarly, a computerprogram may not treat a leverage request as too high with-out human understanding of the investment style behindthe leverage request.

Now let’s discuss a “stress test.” It’s important to under-stand what happens when a chess player decides to sacri-fice some pieces. The sacrifice is intended not to gain spe-cific advantage but to create certain weaknesses in the posi-tion that the player will try to exploit later. A computer willaccept the sacrifice and evaluate the current position in itsfavor, rather than considering the intent of the sacrifice. Asthe game progresses, the computer will treat an extra pieceas a positive, even as its position deteriorates.

Consequently, the computer will not only miss the unex-pected sacrifice but will also be unable to determine wherethe sacrifice would lead. Moreover, it certainly doesn’t giveany thought as to why a human player would want to sac-rifice at all. A human player, in contrast, might not acceptsacrifice in the first place, in order not to be exposed to theopponent’s well-developed strategy.

Despite the fact that the world’s best chess players couldbarely manage to draw their matches against the best com-puter programs, average players are able to achieve decentresults against the same programs by selecting inferioropenings that would be ridiculed if played against otherhumans. The sole purpose of such openings is to createpositions that rely more on deep comprehension of posi-tional nuances than on the rough calculating power ofcomputers.

A human player knows that opening moves made areinferior, and it’s generally just a matter of time until he orshe will eventually take advantage of them. A computerdoesn’t recognize inferiority and has to prove errors bycalculating. If calculations don’t reach far enough, thecomputer won’t select the correct strategy. Based onrecent events, computer risk models, just like computer

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chess models, tend to ignore a piece of analysis that isnot readily calculable — the piece that requires humanunderstanding.

Keep in mind that all scenarios, at least in theory and nomatter how improbable, are available on the chess board.Nevertheless, despite having superior quantitative ability,computers can’t pick them all. So, then, how can theyaccount for all stress scenarios and calculate probabilitiesof events that never happened in finance?

On the other hand, world champion chess players areknown to make simple errors late in games because offatigue and/or mental lapses, and computers do an excel-lent job in avoiding such errors.

The Art of the SacrificeOne last strategy that is worthy of consideration is why aplayer is more likely to sacrifice at the opening of a matchwith black pieces rather than with white pieces. It is impor-tant to remember that with white pieces, he or she alreadyhas the advantage of the first move, and the goal is to keepthat advantage and try to increase it. On the other hand,with black pieces, he or she is already behind, so why notsacrifice? It might help eliminate the first-move advantage.

Thinking about this from a risk management perspec-tive, if a fund is outperforming its benchmark, why usemore leverage? But if it’s underperforming, why not usemore leverage?

A player may resort to sacrifices in time pressure, hopingthat an opponent will make a mistake by calculating. Thebest way to avoid this is to exchange pieces. In the lastgame of the 1985 world championship, the world champi-on had to win to tie the match. From the first move, helaunched an all-out attack. His opponent, Garry Kasparov,expected the attack and prepared in advance. Kasparovwon the game and the title.

In the last game of the 1987 world championship, roleswere reversed. Kasparov, as the world champion, had towin to keep the title. Not only did he not attack, he took awhile to cross the middle of the board and stayed awayfrom exchanging the pieces. His opponent was consequent-ly forced to spend time calculating. Whenever he tried tosimplify the position, Kasparov stayed back. As time beganto run out, Kasparov’s opponent committed a few smallerrors that Kasparov was able to capitalize on, convertingtiny positives into a decisive advantage.

Thus, using very little leverage, the world championretained the crown. This game turned into a very valuablelesson for many players on how to approach must-win situ-ations. The main lesson is that knowledge of an opponent’s

strategy before the game can be crucial to the end result. This type of knowledge can also prove to be quite useful

in risk management. If we can determine, for example,what strategy a portfolio manager will choose next, proac-tive steps can be taken to keep a firm’s current portfolioexposure reasonable (even when current exposure does notseem excessive) and to avoid unnecessary calculations.

When models are insufficient, this knowledge can proveparticularly helpful. Say, for example, a fund sells deepOTM naked puts. A stress-testing model would assign avalue to a downside move and compare it to a fund's equi-ty. However, it wouldn’t know that the probability of themove changes daily, and it also wouldn’t take into accountthat something will always happen in the human world.

Bobby Fischer was perhaps the best chess player ever, butnot the greatest tactician. He proposed FischerRandomchess, which reduces computer knowledge and calculatingpower in general by selecting starting setups at random.Under such conditions, each human player will have moreand less favorable starting setups. A computer won’t makesuch a distinction.

Computer programs are blind to human intentions andmay not evaluate them correctly but do a great job inavoiding simple human blunders. Humans must specifyopponents’ intentions correctly and base computer calcula-tions on those intentions, regardless of whether the oppo-nent is a chess grandmaster or a hedge fund manager.

Different Responses to Different StrategiesIn many ways, risks arising from randomness are the easi-est to manage. If we flip a fair coin 100 times, for a $1 mil-lion bet each time, we know the distribution of outcomesand can plan accordingly. With financial markets, it’s moredifficult, because the parameters of the distribution have tobe estimated.

Risks arising from complex strategic interactions amongcompeting (and in finance, but not chess, cooperating) enti-ties require more subtle management. It is tempting to treateverything as random and then set a powerful computer tocrank through all the calculations. This can work, as com-puter chess programs and successful program tradersdemonstrate. But it doesn’t always work.

Sometimes you have to consider the intentions of otherentities and their responses to your moves. Sometimes thestrategy that can be proven to be optimal with infinite com-puting resources (or perfect information) is a terrible strate-gy in practice. In these situations, a chess master may havebetter insights than a poker, bridge, backgammon or ginrummy champion. ■

✎ IGOR POSTELNIK (FRM) is a national chess master and a vice president in Bear Stearns’s global clearing services risk control group. Hecan be reached at ibpiar300@yahoo.com.